Euclid

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle, the angle contained by the remaining two sides of the triangle is right.

A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.

When the lines containing the angle are straight, the angle is called rectilineal.

A right angle is half of two right angles.

An obtuse angle is that which is greater than a right angle.

An acute angle is that which is less than a right angle.

To place a straight line equal to a given straight line with one end at a given point.

To cut off from the greater of two given unequal straight lines a straight line equal to the less.

If two triangles have two sides and the included angle equal, then they are congruent.

In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines are produced further, the angles under the base are equal to one another.

If in a triangle two angles are equal, then the sides opposite them are equal.

Given two straight lines constructed from the ends of a straight line and meeting in a point, there cannot be constructed from the ends of the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively.

The sum of any two angles of a triangle is less than two right angles.

In any triangle the sum of the three interior angles is equal to two right angles.

The square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

The circle is the plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.

To describe a circle with any centre and distance.

The angle in a semicircle is a right angle.

The ratio of the circumference of a circle to its diameter is constant.